Progress of nuclear theory on studying the neutrinoless double-β decay
Abstract
Neutrinoless double-β decay is at the frontier in the fields of particle physics and nuclear physics.It is a lepton-number violating process and only occurs if neutrinos are Majorana particles.The experimental observation of this decay mode would not only signal the violation of the lepton number but also confirm the Majorana nature of neutrinos, providing crucial insights into the matter dominance in the universe.Moreover, the neutrinoless double-β decay offers a promising way for determining the mass scale and hierarchy of neutrinos.Several experimental projects, including those at China Jinping Underground Laboratory, are actively searching for this novel decay process.The theoretical study of the neutrinoless double-β decay, especially the evaluation of the nuclear matrix element, is pursued energetically by the nuclear physics community.The nuclear matrix elements depend on the decay operators derived from the underlying decay mechanisms and the nuclear many-body wavefunctions obtained from the nuclear many-body approaches.This study reviews the recent progress in the neutrinoless double-β decay from two aspects, the decay operator and the nuclear many-body approaches.Its main purpose is to provide some insights for future studies aiming to realize a reliable evaluation of the nuclear matrix elements.After a brief introduction to the importance of the neutrinoless double-β decay and the nuclear matrix elements, decay operators within the standard light-neutrino-exchange mechanism are derived based on the phenomenological nucleonic currents and the chiral effective field theory.The basic ideas and concepts of various nuclear many-body approaches, including those based on the chiral nuclear force, the renormalized G matrix, the non-relativistic and relativistic density functionals, are illustrated.The achievements and the challenges of the theoretical approaches in calculating the nuclear matrix elements are discussed.The promising ways to constrain the nuclear matrix elements by exploring correlations with other observables are emphasized.The further improvements of the nuclear many-body approaches are also briefly mentioned from the aspects of model space, physical correlations, and implementation of machine learning techniques.
